I have some questions about multilevel LCA/LCR, similar to Example 10.3 in User's Guide. (1) Example 10.3 assumes c#1 and c#2 are related through the common factor f. If I don¡¯t believe this, and delete ¡°f by c#1 c#2¡±, how will Mplus fit the model? Also, how to get output of variance (and/or correlation) of the two random effects in this case?

(2) Is it possible in Mplus that we assume the two random effects are correlated bivariate normal and estimate the model by maximum likelihood with numerical integration? If so, how?

I am using LCA on six math subtest scores with a sample of around 300 children. Those children were from 20 different classrooms. I read from the Mplus manual that Type=COMPLEX can be used to enable corrections to standard errors and chi-square test of model fit for nested data structure.

If my major interest is in number of classes identified instead of significance of path coefficient, is it still important to include Type=COMPLEX? What are the expected consequences when TYPE=COMPLEX is not enabled? Thanks.

Without TYPE=COMPLEX using only the CLUSTER option and not the WEIGHT option, parameter estimates will be correct, standard errors will be underestimated, and chi-square will be overestimated. Note that a minimum of 30-50 clusters is recommended for TYPE=COMPLEX and TYPE=TWOLEVEL.

If you are not concerned with standard errors and chi-square, you can look at the loglikelihood and BIC to determine the number of classes. They are not affected by non-independence of observations due to clustering. TECH11 and TECH14 will not be correct.